Energy Efficient Power Allocation with NOMA in Downlink Heterogeneous Networks
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摘要: 该文针对应用非正交多址接入(NOMA)技术的异构蜂窝网络，在考虑层间层内干扰的情况下，提出一种能效最大化的功率分配算法。该算法主要包括两部分，一部分为子信道内用户功率分配因子的求解，主要利用差分优化的方法，迭代求解。另一部分为子信道间的功率分配，主要利用凹凸程序法将原有的非凸问题简化为可解的凸问题，最后利用拉格朗日求解法得出功率最优解。仿真结果表明该算法有良好的迭代性，且新算法表明利用NOMA技术得到的系统能效较利用正交技术得到的系统能效提高了至少44%以上。Abstract: This paper proposes a power allocation scheme for energy efficiency maximization in a downlink Non-Orthogonal Multiple Access (NOMA)-based Heterogeneous Network (HetNets) with considering the out-of-cell interference and in-cell interference. The scheme contains mainly two parts. One is the power allocation between the users at the same sub-channel, where Difference of Convex (DC) functions -programming is exploited to solve the problem. Another is the power allocation between the sub-channels, in which ConCave–Convex Procedure (CCCP) method and Lagrangian multiplier method are combined to solve the problem. The simulation results show that the fast convergence property, and demonstrate that the EE obtained by the proposed algorithms based on NOMA is at least 44% higher than that obtained by the conventional orthogonal multiple access scheme.
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表 1 子信道内用户功率分配因子算法
DC programing功率分配因子算法 1.初始化：设置${(\alpha _f^n)^c}$的初始值；设置迭代索引$c = 0$；设置最大迭代次数${C_{\max }}$以及容忍度$\mu $的值；计算式
$q({(\alpha _f^n)^0}) = f({(\alpha _f^n)^0}) - g({(\alpha _f^n)^0})$的值。2. repeat 3. 计算式(8)获取最优功率分配因子${(\alpha _f^n)^*}$ 4. $c = c + 1$，${(\alpha _f^n)^c} = {(\alpha _f^n)^*}$，计算$q({(\alpha _f^n)^c}) = f({(\alpha _f^n)^c}) - g({(\alpha _f^n)^c})$ 5. until $\left| {q({{(\alpha _f^n)}^c}) - q({{(\alpha _f^n)}^{c - 1}})} \right| \le \mu $ or $c > {C_{\max }}$ 6. ${(\alpha _f^n)^*} = {(\alpha _f^n)^c}$ 
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表 2 子信道间功率分配算法
CCCP信道功率分配算法 1：初始化 设置迭代索引$v = 0$，误差容忍度$\xi > 0$。设置初始化${{{P}}^0}$，最大迭代次数${V_{\max }}$，计算${\left( {\lambda _f^n} \right)^0} = {1 / {\left( {{{\left( {p_f^n} \right)}^0} + {p_c}} \right)}}$,
${(\gamma _f^n)^0} = {{R_f^n\left( {{{(p_f^n)}^0}} \right)} / {\left( {{{(p_f^n)}^0} + {p_c}} \right)}}$2: repeat 3：利用拉格朗日对偶求解${\left( {{{{P}}^*}} \right)^v}$即${{{P}}^{v + 1}}$其中${\left( {{{{P}}^*}} \right)^v}$满足式(35)和式(36)。 4：根据式(12)更新${(\lambda _f^n)^{v + 1}}$和${(\gamma _f^n)^{v + 1}}$的值。 5：设置$v = v + 1$
6: until $\left| {\mathop {\max }\limits_{{P} } \left\{ {\displaystyle\sum\limits_{f = 1}^F { { {(\lambda _f^n)}^v}[R_f^n({ {(p_f^n)}^v})(1 + { {\beta \left( { { {(p_f^n)}^v} + {p_c} } \right)} / B}) - { {(\gamma _f^n)}^v}({ {(p_f^n)}^v} + {p_c})]} } \right\} } \right| \le \xi$ or $v > {V_{\max }}$
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